CN114650657A

CN114650657A - Method and system for generating and updating positioning distribution map

Info

Publication number: CN114650657A
Application number: CN202110102239.XA
Authority: CN
Inventors: 曾绍崟; 陈建伟
Original assignee: Industrial Technology Research Institute ITRI
Current assignee: Industrial Technology Research Institute ITRI
Priority date: 2020-12-18
Filing date: 2021-01-26
Publication date: 2022-06-21
Anticipated expiration: 2041-01-26
Also published as: TWI746320B; US20220197263A1; TW202226159A; US11687065B2; CN114650657B

Abstract

A method of generating and updating a histogram, comprising: the method comprises the steps of generating a positioning distribution diagram according to a circuit diagram and an exposure pattern, carrying out exposure simulation according to the positioning distribution diagram to generate an exposure result diagram, comparing the circuit diagram with the exposure result diagram to generate a plurality of candidate error distribution diagrams, selecting one of the candidate error distribution diagrams as an error distribution diagram, and carrying out 0-1 integer programming operation according to error pixels of the circuit diagram and the error distribution diagram to update the positioning distribution diagram, wherein the updated positioning distribution diagram is associated with the error distribution diagram.

Description

Method and system for generating and updating positioning distribution map

Technical Field

The invention relates to a method and a system for generating and updating a positioning distribution map.

Background

The Printed Circuit Board (PCB) industry and the touch panel industry have been developed and used more and more. With the enhancement of the computing power of the cpu of the electronic product, the structure of the electronic device becomes more and more complex, the number of required components increases, and the more, thinner, shorter, and smaller, the more dense the circuits and components on the pcb are. Therefore, the width and distance between the conductive wires on the printed circuit board are getting smaller and smaller. In the future circuit board market, the line width or pitch may be as fine as 150 microns (mum) to 10 microns, and the next generation product design may be even as fine as 5 microns or less. As the printed circuit board tends to be developed toward a High Density Interconnect (HDI) board or a multi-layer board, the requirements for the line width and the alignment precision of the circuit on the printed circuit board are higher and higher, and thus, the emerging direct imaging technology is also more and more emphasized by the industry.

Disclosure of Invention

Accordingly, the present invention provides a method and system for generating and updating a histogram, so as to achieve a small circuit line width by exposing a large-sized laser spot.

According to an embodiment of the present invention, a method for generating and updating a histogram includes: generating at least one positioning distribution map according to a circuit diagram and at least one exposure pattern, wherein the circuit diagram comprises a plurality of target pixels and a plurality of background pixels, each positioning distribution map comprises a plurality of positioning points, and the positioning points are positioned in a plurality of the target pixels and are related to the exposure pattern; performing an exposure simulation according to each of the at least one positioning distribution map to generate at least one exposure result map, wherein the exposure simulation comprises simulating to emit a virtual light spot by each of the positioning points of each of the at least one positioning distribution map to generate at least one exposure result map; comparing the circuit diagram with the at least one exposure result diagram to generate at least one candidate error distribution diagram; selecting one of the at least one candidate error distribution map as an error distribution map, wherein the error distribution map comprises a plurality of error pixels; performing a 0-1 integer programming operation according to the circuit diagram and at least one of the error pixels to update one of the at least one localization profile, wherein the updated localization profile includes a plurality of modified localization points, and the updated localization profile is associated with the selected candidate error distribution map.

A system for generating and updating a histogram according to an embodiment of the present invention includes: a non-transitory machine-readable storage device storing a plurality of instructions; and a processing device electrically coupled to the non-transitory machine-readable storage device, the processing device executing the instructions and causing operations comprising: generating at least one positioning distribution map according to a circuit diagram and at least one exposure pattern, wherein the circuit diagram comprises a plurality of target pixels and a plurality of background pixels, each positioning distribution map comprises a plurality of positioning points, and the positioning points are positioned in a plurality of the target pixels and are related to the exposure pattern; performing an exposure simulation according to each of the at least one positioning distribution map to generate at least one exposure result map, wherein the exposure simulation comprises simulating to emit a virtual light spot by each of the positioning points of each of the at least one positioning distribution map to generate at least one exposure result map; comparing the circuit diagram with the at least one exposure result diagram to generate at least one candidate error distribution diagram; selecting one of the at least one candidate error distribution map as an error distribution map, wherein the error distribution map comprises a plurality of error pixels; performing a 0-1 integer programming operation according to the circuit diagram and at least one of the error pixels to update one of the at least one localization profile, wherein the updated localization profile includes a plurality of modified localization points, and the updated localization profile is associated with the selected candidate error distribution map.

In summary, the method and system for generating and updating the histogram of the present invention pre-find the initial position map of the light spot through the exposure simulation, and apply the connected-Component Labeling (CCL) and the parallelized integer programming operation, thereby effectively reducing the operation amount and speeding up the calculation. The invention can realize the exposure by using the light spots with the size larger than the line width so as to meet the precision requirements of fine line width and line distance.

Drawings

FIG. 1 is a flow chart of a method of generating and updating a histogram in accordance with one embodiment of the present invention;

FIG. 2 is an exemplary diagram of a circuit diagram;

FIG. 3 is a simplified exemplary diagram of a circuit diagram;

FIG. 4 is an exemplary diagram of an exposure pattern;

fig. 5 is a detailed flowchart of step S1 of fig. 1;

FIG. 6 is an exemplary diagram of step S11 of FIG. 5;

FIG. 7 is an exemplary diagram of step S12 of FIG. 5;

FIGS. 8 and 9 are diagrams illustrating two examples of exposure patterns and their positioning points;

FIG. 10A is a diagram of four exemplary exposure patterns with a length and width of 3 pixels;

FIG. 10B is a schematic diagram of the tiling of planar regions in the four exposure patterns of FIG. 10A;

FIG. 11A is a diagram of six exemplary exposure patterns with 4 pixels in both length and width;

FIG. 11B is a schematic diagram of the tiling of planar regions with the six exposure patterns of FIG. 11A;

FIG. 12 is a flowchart of a first embodiment of step S5 of FIG. 1;

FIG. 13A is a simplified schematic diagram of a circuit;

FIG. 13B is a diagram illustrating an error distribution according to the method selected in step S4 of FIG. 1 and FIG. 13A;

FIG. 13C is a schematic diagram of an error pixel and a correction pixel;

FIG. 14 is a schematic diagram of determining a verification pixel based on the modified pixel of FIG. 13C;

FIG. 15 is a flowchart of a second embodiment of step S5 of FIG. 1;

fig. 16 is an exemplary diagram of a pixel group;

FIG. 17 is a schematic diagram of determining a verification pixel based on the modified pixel of FIG. 16;

FIG. 18 is a flowchart of a third embodiment of step S5 of FIG. 1;

FIG. 19 is a partial schematic view of a large pixel cluster; and

FIG. 20 is a block diagram of a system for generating and updating a histogram in accordance with an embodiment of the present invention.

Description of reference numerals:

S1-S5, S11-S12, S51-S57, S61-S67, S71-S78 …

A 0-plane area;

a1 — target shape;

B21-B23, B31-B34, B41-B46-exposure patterns;

P₆、P₉、P₁₄XA, XB, X-error pixel;

P₁～P₁₈、FA₁～FA₈、FB₁～FB₈f-correction pixel;

P₁～P₁₈v-verification pixel;

1-a non-transitory machine-readable storage device;

3-treatment device.

Detailed Description

In order that the objects, technical solutions and advantages of the present invention will become more apparent, the present invention will be further described in detail with reference to the accompanying drawings in conjunction with the following specific embodiments.

The digital direct imaging exposure machine directly images Computer-Aided manufacturing (CAM) data on a substrate of a printed circuit board, so that a negative film program in an exposure process can be omitted, deviation caused by negative film expansion and contraction is reduced, and the yield of the printed circuit board production is improved.

In a digital direct imaging system having a laser array, in order to obtain a high-quality exposure image, in addition to precisely controlling and correcting the scan timing, the uniformity of the power of the laser array also affects the image quality. One way is to detect and adjust the laser power output with a power meter, however, the exposure results may exhibit partial non-uniformity phenomena involving individual laser spot profile and photoresist threshold effects at higher precision imaging quality requirements. The laser array system has the light spot distribution of different laser sources, even if each laser source has the same power, the distribution is not easy to be consistent, and when the precision requirement is pushed to the limit, even if the laser array system is an ideal laser spot, the essence of the laser array system also has complex light spot distribution and characteristics in the optical physics, and the laser array system is difficult to be regarded as a simple mathematical model. In addition, as the line width of the circuit pattern is continuously thinned, a thinner light spot is required for exposing a thin line width, but since the laser light spot cannot be reduced all the time in violation of physical limitation, when the line width of the circuit pattern is reduced to be smaller than the light spot, insufficient exposure precision may be caused.

The method and system for generating and updating the positioning distribution map provided by the invention are suitable for pre-calculating the positioning distribution map before the laser direct imaging exposure machine processes the printed circuit board. The histogram is used to indicate whether the pixels at each position in the circuit diagram need to be exposed.

FIG. 1 is a flowchart of a method for generating and updating a histogram according to an embodiment of the invention. Step S1 is generating at least one anchor point map according to a circuit diagram and at least one exposure pattern, wherein the circuit diagram includes a plurality of target pixels and a plurality of background pixels, each of the at least one anchor point map includes a plurality of anchor points, and the anchor points are located in a plurality of the target pixels and are associated with the exposure pattern. Please note that step S1 and the references to "at least one" hereinafter generally refer to one or more.

The target pixels and the background pixels are arranged in a matrix form, for example. In one embodiment, the target pixel forms a circuit structure and the background pixel forms a substrate structure. Fig. 2 is an example of a circuit diagram in which a white portion is formed by a plurality of target pixels and a black portion is formed by a plurality of background pixels. Each of the target pixels and the background pixels has an exposure state, the exposure state of each target pixel is a high exposure, and the exposure state of each background pixel is a low exposure.

In one embodiment, the dose threshold is the minimum amount of energy to harden the photosensitive material during exposure. If the exposure dose value required by a pixel exceeds the dose threshold, the exposure state of the pixel is high exposure. If the exposure dose value required by a pixel is less than the dose threshold, the exposure state of the pixel is a low exposure. Fig. 3 is an example of a simplified version of a circuit diagram, each square representing a pixel, a white square representing a background pixel, a colored square representing an object pixel, and a plane area a0 of the circuit diagram being 81 pixels, of which 45 object pixels constitute a T-shaped object shape a1 and represent a circuit structure.

The exposure pattern provides a basic rule for arranging anchor points on the circuit diagram. Fig. 4 is an example of the exposure pattern B21. The planar area occupied by the exposure pattern B21 of FIG. 4 is referred to as a base area, which in one embodiment is 2 pixels in length and width. The black dots in the exposure pattern B21 represent anchor points. The "at least one exposure pattern" in step S1 may be a fixed exposure pattern or a plurality of candidate exposure patterns. How step S1 generates a histogram according to the circuit diagram of fig. 3 and the exposure pattern of fig. 4 is described first, and then a plurality of candidate exposure patterns are described.

Fig. 5 is a detailed flowchart of step S1 of fig. 1, step S11 is "confirming an exposure pattern in a target shape", and fig. 6 is an example of step S11. Starting from the top left corner, the example of fig. 6 spreads exposure pattern B21 across the entire planar area a0 in a left-to-right and top-to-bottom manner, as indicated by the bold line squares. The pixels at the lower and right boundaries of the plane area a0 are laid out using part of the basic area so as not to exceed the boundaries.

Step S12 is "mark anchor point in target shape", and fig. 7 is an example of step S12. The object shape a1 is a colored square grid in fig. 7. For the exposure pattern B21 superimposed on the target shape a1, the anchor points are marked at the target pixels in the target shape a1 in accordance with the anchor points configured in the exposure pattern B21. Fig. 7 shows all anchor points located in the target pixel, which form an anchor distribution map. The localization map includes a plurality of localization points located at a plurality of the target pixels.

In one embodiment of the present invention, the exposure pattern having the length and width of the basic region of k pixels is referred to as a k × k exposure pattern. The present invention does not limit the value of k. For example, each target pixel of the histogram generated according to the 1 × 1 exposure pattern indicates the anchor point. Fig. 8 and 9 show two other examples of exposure patterns B22 and B23, and anchor point profiles generated according to the two examples. FIG. 10A is four examples of 3 × 3 exposure patterns B31-B34. FIG. 10B is a schematic illustration of the four examples B31-B34 of the 3 × 3 exposure pattern of FIG. 10A tiling the entire planar area A0. FIG. 11A is six examples B41-B46 of 4 × 4 exposure patterns. FIG. 11B is a schematic diagram of six examples B41-B46 of the 4 × 4 exposure pattern of FIG. 11A tiling the entire planar area A0. In other examples of exposure patterns, the length and width of the base regions may be different.

The present invention is not limited to the arrangement of the plurality of anchor points in the anchor map. In an embodiment, a distance between two anchor points of the plurality of anchor points is not less than a length or a width of one target pixel. In other words, two anchor points are spaced apart by more than one pixel in the horizontal direction, or two anchor points are spaced apart by more than one pixel in the vertical direction. For example, in fig. 10B, two anchor points on the same column are spaced by 2 pixels in accordance with the planar area a0 arranged in accordance with the exposure pattern B31. For example, in fig. 11B, two anchor points on the same column are spaced by 3 pixels in accordance with the planar area a0 arranged in accordance with the exposure pattern B45.

Referring back to fig. 1, step S2 is "performing an exposure simulation according to each of the at least one histogram to generate at least one exposure result map". The exposure simulation includes simulating emission of a virtual light spot with each of the anchor points of each of the at least one anchor profile to generate at least one exposure result map. The exposure simulation is to simulate a virtual laser source by software, and the virtual laser source emits a virtual light spot according to each positioning point in the positioning distribution diagram, so as to simulate the exposure behavior of the actual laser source and generate an exposure result diagram.

In one embodiment, the number of exposure patterns, the number of histograms, and the number of exposure result maps are all equal. In step S1, an exposure pattern is used to generate a histogram, and in step S2, an exposure result map is generated according to the histogram. In step S1, a plurality of histograms are generated by using a plurality of candidate exposure patterns, and a plurality of exposure result maps are generated in step S2.

In one embodiment, the length or width of each of the target pixel and the background pixel is less than the diameter of the virtual light spot, in other words, the diameter of the virtual light spot is greater than the size of any pixel in the circuit diagram; however, the present invention is not limited thereto.

One exposure result image comprises a plurality of test exposure results, and each test exposure result corresponds to one of the target pixel and the background pixel. In other words, the exposure result graph and the circuit diagram are substantially the same in format, and the difference is that: the value of each pixel in the circuit diagram represents the expected exposure dose value received by the pixel, and the value of each pixel in the exposure result diagram represents the dose accumulated value of the pixel after exposure simulation. In an embodiment, since the area of one virtual spot is larger than the area of one pixel, if the distance between two positioning points is not larger than the spot diameter, two virtual spots emitted according to the two positioning points have an overlapping region, and the pixels located in the overlapping region will include the dose accumulation of the two virtual spots.

Referring back to fig. 1, step S3 is "comparing the circuit diagram with the at least one exposure result diagram to generate at least one candidate error distribution map", and step S4 is "selecting one of the at least one candidate error distribution map as an error distribution map", wherein the error distribution map includes a plurality of error pixels.

The number of candidate error profiles depends on the number of exposure patterns, and if one exposure pattern is used in step S1, step S3 generates one candidate error profile based on one exposure result profile generated in step S2, and the error profile generated in step S4 is the candidate error profile of step S3. The following first describes the format of the error distribution map, and then describes how to generate the candidate error distribution map in step S3, and further describes how to select one of the candidate error distribution maps generated in step S3 as the error distribution map in step S4.

The error distribution map comprises a plurality of error pixels, each error pixel corresponding to one of the trial exposure results. It is mentioned that each trial exposure corresponds to one of the target pixel and the background pixel, and thus the error pixel also corresponds to one of the target pixel and the background pixel. When the error pixel corresponds to the target pixel, the trial exposure result corresponding to the error pixel is low exposure. When the error pixel corresponds to the background pixel, the trial exposure result corresponding to the error pixel is the high exposure. In other words, the error pixels include those target pixels that are expected to be exposed but not actually successfully exposed, and those background pixels that are expected not to be exposed but are actually exposed.

The candidate error profiles are generated, for example: and comparing each test exposure result of the exposure result map one by one according to the exposure state of each pixel of the circuit map. For example: the exposure state of each pixel in the circuit diagram is subjected to binarization operation to generate a first matrix, each trial exposure result in the exposure result diagram is subjected to binarization operation to generate a second matrix, and the first matrix and the second matrix are subjected to logical Exclusive-OR (XOR) operation to generate an error distribution diagram. The error distribution map generated according to the above example is a Boolean (Boolean) matrix, and the matrix element values for error pixels are 1 and the matrix element values for non-error pixels are 0. The binarization operation in the above example includes the following two notation ways: if the accumulated dose value of the pixel is greater than or equal to the dose threshold, it is marked as 1, and if the accumulated dose value of the pixel is less than the dose threshold, it is marked as 0.

If the at least one exposure pattern in step S1 is a plurality of candidate exposure patterns, for example, including B21 to B23 in fig. 4, 8 and 9, B31 to B34 in fig. 10A, and B41 to B46 in fig. 11A, step S1 generates a plurality of localization profiles, step S2 generates a plurality of exposure result maps, and step S3 generates a plurality of candidate error profiles, each of which has a plurality of error pixel numbers. Therefore, in an embodiment of step S4, a minimum value of the error pixel numbers is selected, and one of the at least one candidate error distribution map corresponding to the error pixel number with the minimum value is used as the error distribution map. In short, step S4 selects a candidate error distribution map having the smallest number of error pixels as the error distribution map.

For example, if the 1 × 1 exposure pattern and the plurality of candidate exposure patterns B21 to B46 in fig. 4 and 8 to 11 are adopted in step S1, the number of the plurality of error pixels calculated in step S4 is shown in the following table one.

Table one

Candidate exposure patterns	Number of error pixels	Candidate exposure patterns	Number of error pixels
				1 × 1 Exposure Pattern	5819942	B34	203323 (minimum)
B21	2347445	B41	5135068
				B22	1847766	B42	5455178
B23	2783945	B43	4536068
				B31	1540662	B44	5496023
B32	1534771	B45	5135068
				B33	919520	B46	5051078

The smaller the number of error pixels represents the less amount of calculation required for the subsequent step. As can be seen from table one, the candidate error distribution map generated using the candidate exposure pattern B34 has the least error pixels. Therefore, in the following steps, the candidate error distribution map corresponding to the candidate exposure pattern B34 is processed as an error distribution map.

Referring back to fig. 1, step S5 is "perform a 0-1 integer program operation according to the circuit diagram and at least one of the error pixels to update one of the at least one localization profile", in which the updated localization profile includes a plurality of modified localization points, and the updated localization profile is associated with the selected candidate error distribution map. Step S5 basically includes the following three stages. The first stage is as follows: selecting the at least one error pixel of the error profile to perform a dilation operation to determine a plurality of modified pixels in the at least one location profile. And a second stage: "perform the dilation operation to determine a plurality of verification pixels in at least one of the positioning profiles according to each of the correction pixels". And a third stage: performing the 0-1 integer programming operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the one of the at least one histogram.

Three embodiments of step S5 are described below, the first embodiment dealing with at least one error pixel in the error profile. The second embodiment deals with a pixel group in the error distribution map, the pixel group includes a plurality of error pixels, and a plurality of corrected pixels obtained by performing dilation operation on the error pixels have a connected property. The third embodiment deals with the pixel group as described in the second embodiment, and the number of pixels in the pixel group exceeds the maximum computation amount of the designated processor, so the third embodiment further includes a mechanism for batch processing a plurality of pixels in a large pixel group. In the third embodiment, the number of batches and the number of pixels in each batch depend on the processing capability of hardware such as a processor and a memory, and the invention is not particularly limited.

Fig. 12 is a flowchart of a first embodiment of step S5 of fig. 1. In an embodiment, the process of fig. 12 may be repeatedly executed a plurality of times according to the number of error pixels, or the process of fig. 12 may be executed by a plurality of processors simultaneously, which is not limited in the present invention. Steps S51 and S52 in fig. 12 correspond to the first stage, step S53 corresponds to the second stage, and steps S54 to S57 correspond to the third stage.

Step S51 is "select the at least one error pixel of the error profile". In one embodiment, if the distance between the error pixels selected at the same time is larger than the spot diameter, the step S51 can be performed by parallelization.

Step S52 is "perform a dilation operation according to the at least one of the error pixels to determine a plurality of corrected pixels in the histogram". The expansion (dilation) operation is performed by taking each error pixel as a center of a circle, and all pixels covered in the spot radius are regarded as correction pixels in the positioning distribution map. The correction pixels include error pixels. Each correction pixel is located at a distance from the error pixel that is not greater than the radius of the virtual spot.

Fig. 13A is a simplified circuit diagram example in which squares within a T-shape enclosed by thick lines represent target pixels. FIG. 13B is an example of the error distribution map selected according to the method of FIG. 13A and the step S4, wherein the index P is₆、P₉And P₁₄The squares of (a) represent error pixels. After steps S51-S52 are performed according to FIG. 13B, FIG. 13C is a schematic diagram of an error pixel and a correction pixel, wherein P is labeled₁～P₅、P₇～P₈、P₁₀～P₁₃And P₁₅～P₁₈The squares of (a) represent the correction pixels other than the error pixels, in other words, the correction pixels include P₁～P₁₈. Therein, theIn the embodiment, the spot radius is a length or a width of 1 pixel, but the invention is not limited thereto.

Step S53 is "perform the dilation operation to determine verification pixels in the histogram according to each of the correction pixels". The dilation operation in step S53 is performed for each correction pixel P₁～P₁₈As a center of circle, all pixels covered within the spot radius are regarded as verification pixels in the positioning distribution map, and the verification pixels include at least one error pixel P selected in step S51₆、P₉And P₁₄And the corrected pixel P determined in step S52₁～P₅、P₇～P₈、P₁₀～P₁₃And P₁₅～P₁₈. Each verification pixel is no further from one of the correction pixels than the radius of the virtual spot. FIG. 14 is a schematic diagram of determining verification pixels based on the correction pixels of FIG. 13C, wherein the squares denoted by V are the verification pixels except for the error pixels and the correction pixels, i.e., the verification pixels include the error pixels and the correction pixels P₁～P₁₈And all pixels labeled V.

In step S54, a "fixed-point allocation is generated according to the at least one error pixel and the correction pixels". In one embodiment of step S54, the anchor point configuration includes a plurality of specified configuration values, each configuration value indicating whether a modified pixel or an error pixel is an anchor point. Based on the example of fig. 14, step S54 generates a 0-1 matrix with 18 columns and 1 rows to represent the 18 modified pixels P in fig. 13₁～P_18-The anchor point configuration. An element in the matrix represents a configuration value of an anchor point, a configuration value of 1 represents that, for example, a pixel corresponding to the matrix element is set as an anchor point, and a configuration value of 0 represents that, for example, a pixel corresponding to the matrix element is not set as an anchor point. For example: if the 0-1 matrix is [ 110011000000000000 ]]^T _18×1Representative of the correction pixel P₁、P₂、P₅、P₆Is set as an anchor point, and the remaining modified pixels P₃、P₄、P₇、P₈～P₁₈Is not set as an anchor point. Matrix elements in the above examplesRespectively corresponding to the correction pixels P from top to bottom₁～P₁₈However, the invention is not limited to the corresponding relationship between the correction pixels and the matrix elements. In another embodiment of step S54, the pixel P is corrected₁～P₁₈Is a matrix with 18 variables, as follows: [ X ]₁ X₂ X₃ … X₁₈]^T _18×1Each element X in the matrix has a value of 0 or 1, and these variables are solved in step S55.

Step S55 is executed to perform the 0-1 integer program operation according to the modified pixels and the anchor point configuration to generate a plurality of modified results. Each correction result indicates whether each of the error pixel, the correction pixel, and the verification pixel is a high exposure or a low exposure. Step S56 is "compare each of the corrected results with one of the exposure states of the circuit diagram to generate a comparison result indicating whether the comparison result is qualified".

For example, the dose threshold for the target pixel is 22, and the spot window matrix is as follows:

in one embodiment, the 0-1 integer program operation is performed for each verification pixel V and P, for example, using a spot window matrix₁～P₁₈An inner product and operation is performed to obtain a dose integrated value (correction result) of the verification pixel. For example to calculate the verification pixel P₁₄Dose cumulative value D of₁₄The equation of (1) is:

D₁₄＝0.34*P₉+2.49*P₁₀+0.34*P₁₁+2.49*P₁₃₊18.4*P₁₄+2.49*P₁₅+0.34*P₁₆+2.49*P₁₇+0.34*P₁₈

in one embodiment, since step S54 has specified a plurality of configuration values of the setpoint configuration, the dose cumulative value D can be obtained by substituting the configuration values corresponding to the above formula₁₄. Due to the verification of the pixel P₁₄Belongs to the target pixel, so its dose integrated value D₁₄It is required to be greater than the dose threshold 22.

Calculating another verification pixel V_(1，3)Dose cumulative value D of_(1，3)The equation of (1) is:

D_(1，3)＝0.34*A_(0，2)+2.49*A_(1，2)+0.34*V_(2，2)+2.49*A_(0，3)+18.4*V_(1，3)+2.49*V_(2，3)+0.34*A_(0，4)+2.49*V_(1，4)+0.34*P₁

wherein V_(x，y)Representing a verification pixel V with x as a horizontal coordinate and y as a vertical coordinate. A. the_((x，y)Representing non-verification pixels with x as the horizontal coordinate and y as the vertical coordinate. Whether the non-verification pixel a is an anchor point depends on the anchor distribution map of step S2. The setpoint configuration of step S54 and the setpoint profile of step S2 are substituted into the equation to obtain the cumulative dose value D_(1，3). Since the pixel V is verified_(1，3)Belongs to the background pixel, so the dose accumulated value D is_(1，3)It is less than or equal to the dose threshold 22.

In the present embodiment, the anchor point configuration specified in step S54 allows each verification pixel V and P to be configured₁～P₁₈If the accumulated dose value meets the corresponding dose threshold, step S56 generates a comparison result indicating a pass. Otherwise, go back to step S54 to generate another setpoint configuration, and then repeat the flow of steps S55-S56.

In another embodiment, all verification pixels V and P are represented in a matrix operation with AX ≦ B₁～P₁₈Calculation of the dose integrated value (40 pixels in total in this example). Wherein the matrix X is the modified pixel P provided in step S53₁～P_18-The matrix in terms of variables is as follows: [ X ]₁ X₂ X₃… X₁₈]^T _18×1. Matrix B is a dose threshold matrix, shown below [ 222222 … 22 ]]^T _40×1. The values of the elements in matrix B are determined by the circuit diagram. Matrix A is a light spot window to traverse all verification pixels V and P₁～P₁₈The resulting coefficient matrix is shown in Table two below, in whichThe negative number table represents that the column coefficient should make the accumulated dose value of the verification pixel larger than the dose threshold, so the modified coefficient is negative after the shift operation is adopted.

Table two

In another embodiment of steps S55-S56, the matrix operation with AX ≦ B is used to solve the modified pixel matrix X using 0-1 integer programming. Thus, a plurality of correction results can be obtained, one for each correction pixel P in the matrix X₁～P₁₈。

Step S56 is "compare each of the corrected results with one of the exposure states of the circuit diagram to generate a comparison result indicating whether the comparison result is qualified". The "one of the exposure states of the circuit diagram" corresponds to one of the error pixel, the correction pixel, and the verification pixel. Step S56 determines whether the correction result for each pixel (i.e., the exposure status for each error pixel, each correction pixel, and each verification pixel) matches the exposure status for the pixel in the circuit diagram. In one embodiment, if the correction result of each pixel matches the corresponding exposure status, it means that the anchor point configuration used for the correction eliminates the error pixel while ensuring the correctness of the verification pixel, so the comparison result of step S56 is yes, and step S57 is continued to be executed to update the at least one anchor point in the at least one anchor point distribution map according to the comparison result and the anchor point configuration. The updated localization point map includes a plurality of modified localization points, and the modified localization points may be different from the localization points of step S12, for example, in the updated localization point map, the positions of the localization points of the previous step S12 may not be modified localization points; for another example, in the updated localization profile, the position that was not the localization point originally in step S12 may become a modified localization point; for another example, in the updated localization map, the position originally being the localization point in step S12 is still the modified localization point. In another embodiment, the modified result satisfying all pixels may not be found, so that the step S56 can generate the comparison result indicating qualified when the "number of non-conforming pixels is less than a threshold". In another embodiment, if all combined anchor point configurations are enumerated, it is possible to obtain a plurality of suitable anchor point configurations. In an embodiment of the present invention, the suitable positioning point configuration obtained for the first time is used as a basis for updating the positioning distribution map, so as to speed up the overall process. If the comparison result in step S56 is "no", then the process returns to step S53, another anchor point configuration is replaced, and the flow of steps S54 to S56 is executed again to obtain an appropriate anchor point configuration.

Fig. 15 is a flowchart of a second embodiment of step S5 of fig. 1. In an embodiment, the process of fig. 15 may be repeatedly executed multiple times according to the number of pixel groups, or the process of fig. 15 may be executed simultaneously for multiple pixel groups by multiple processors, which is not limited in the invention.

In step S61, the dilation operation is performed according to each of the error pixels of the error map to determine the correction pixels in the histogram. Step S61 is similar to step S52, in one embodiment, step S52 performs dilation on one error pixel, and step S61 performs dilation on all error pixels respectively.

In step S62, a "link component marking procedure is performed according to each of the modified pixels to determine a plurality of pixel groups". In one embodiment, the dilation operation of step S61 is performed before the clustering determination of step S62 to determine the range of each pixel cluster. Each correction pixel of each pixel group is no further from one of the error pixels than the radius of the virtual spot. The pixel group comprises a plurality of modified pixels in the modified pixels, and the modified pixels of the pixel group have a connectivity property, such as two pixels sharing a same boundary with each other, that is, two pixels are adjacent to each other. A Connected Component Labeling (CCL) program is used to label each connected component area in a binary image with a specific label, where the connected component area is composed of adjacent modified pixels or adjacent error pixels.

FIG. 16 shows a pixel groupAn example, squares labeled XA and XB represent error pixels, labeled FA₁～FA₈The square grid of (b) represents a correction pixel belonging to the error pixel XA, denoted FB₁～FB₈The square grid of (a) represents the correction pixels belonging to the error pixel XB. Three correction pixels FA located to the right of the error pixel XA in fig. 16₁、FA₄、FA₇Each of which is associated with three correction pixels FB located to the left of the error pixel XB₁、FB₄、FB₇Are adjacent, so that these correction pixels have a connected property. Executing the connected component labeling procedure according to all the modified pixels can determine a plurality of independent pixel groups, and any two pixel groups do not have connected property.

In step S63, the dilation operation is performed to determine the verification pixels in the histogram according to each of the pixel groups. Each of the correction pixels of the pixel group is not farther from one of the error pixels than the radius of the virtual spot. Step S63 is similar to step S54, in one embodiment, step S54 performs dilation on each of all modified pixels, and step S63 performs dilation on all modified pixels in each pixel group. Fig. 17 is a schematic diagram of determining verification pixels based on the corrected pixels of fig. 16, and the squares denoted by V are verification pixels except for error pixels and corrected pixels.

In step S64, a "fixed-point allocation is generated according to each error pixel and each correction pixel in each pixel group". Step S64 is similar to step S53, in one embodiment, step S53 generates an anchor point configuration for all modified pixels, and step S64 generates an anchor point configuration for the error pixels and the modified pixels in each pixel group, so that step S64 generates a plurality of anchor point configurations corresponding to the plurality of pixel groups. One anchor point configuration generated in step S64 is associated with all the modified pixels in one pixel group. Based on the example of fig. 16, step S64 generates a matrix of 18 columns and 1 rows representing the 18 modified pixels FA in fig. 16₁～FA₈、XA、FB₁～FB₈And XB. Said matrix being for example [ X ]₁ X₂ X₃ … X₁₈]^T _18×1Wherein X is₁～X₈Respectively correspond to FA₁～FA₈，X₉Corresponding to XA, X₁₀～X₁₇Respectively correspond to FB₁～FB₈，X₁₈Corresponding to XB.

In step S65, the 0-1 integer program operation is performed according to each of the pixel groups and each of the anchor point configurations to generate a plurality of modified results. Step S65 is similar to step S55, in one embodiment, step S55 performs a 0-1 integer program operation on an anchor configuration corresponding to each error pixel, and step S65 performs a 0-1 integer program operation on an anchor configuration corresponding to each pixel group.

Step S66 is "compare each of the correction results of each of the pixel groups with one of the exposure states of the circuit diagram to generate a comparison result", and step S67 is "update the positioning distribution map according to the comparison results and the positioning point allocation of each of the pixel groups". The flow of steps S66-S67 is similar to the flow of steps S56-S57, and the flow returning from step S66 to step S64 is similar to the flow returning from step S56 to step S53, in one embodiment, steps S56-S57 process pixels, and steps S66-S67 process pixels according to pixel groups.

In the second embodiment of step S5 of fig. 1, the correction pixels are divided into a plurality of pixel groups for independent calculation using the connected component flag at step S62. Since the spot radius has a certain size, the dose integrated values of the correction pixels around the error pixel affect each other. Modified pixels with connected properties within a pixel group are cross-coupled (coupled) to each other and have coherence (coherence), which is less likely to be individually extracted for integer 0-1 programming operations. A plurality of independent pixel groups can be determined by utilizing a connected component marking program, and the pixel groups are suitable for parallelization to carry out 0-1 integer programming operation, so that the efficiency of error pixel correction can be improved.

The dimensionality of the matrix operation is limited by the hardware capabilities. In other words, when the processor performs the 0-1 integer programming operation according to the anchor point configuration, the "maximum operation amount" of the processor determines the number of the modified pixels that can be operated at a time in the anchor point configuration. In one embodiment, the maximum operand is the number of pixels that the processor can process at one time; in another embodiment, the maximum computation amount is set by the user, and the value of the maximum computation amount does not exceed the computation capability of the processor. In the second embodiment of step S5 of fig. 1, all error pixels and correction pixels in one pixel group are processed at a time by the processor. If the processor cannot process all the modified pixels in one pixel group at a time or the user wants to speed up the overall processing flow, the third embodiment of step S5 can be adopted. Fig. 18 is a flowchart of a third embodiment of step S5 of fig. 1, in which the flow of steps S71 to S73 is similar to the flow of steps S61 to S63. Note that, when the "correction pixel" is referred to, the pixels located around the error pixel determined by the dilation operation and the error pixel itself are referred to, if not specifically mentioned.

In step S74, a first anchor point configuration and a second anchor point configuration in each of the pixel groups are determined according to a maximum computation. Step S74 is similar to step S64 of the second embodiment, and in step S74 of the third embodiment, the "anchor point configuration" can be divided into a dynamic configuration part and a static allocation part. The number of modified pixels of the dynamic allocation portion is determined by the configuration of the first anchor point, and the number of modified pixels of the static allocation portion is determined by the configuration of the second anchor point. The first positioning point configuration comprises a plurality of first configuration values, and the first configuration values are dynamically adjusted in the 0-1 integer programming operation of step S75. The second anchor point configuration comprises a plurality of second configuration values, and the second configuration values are set to fixed default values in the 0-1 integer programming operation of step S75. The total quantity of the first configuration value and the second configuration value is related to the maximum operation quantity one by one; in an embodiment, the total number of the first configuration value and the second configuration value is less than or equal to the maximum operation amount.

Please refer to fig. 19, which is a partial schematic view of a large pixel group. In one embodiment, assuming the maximum amount of operation of the processor is 20 pixels, the processor cannot correct all of the corrected pixels F, X in FIG. 19 in one operation. Therefore, when step S74 of the third embodiment is executed for a large pixel group in which the number of correction pixels exceeds the maximum computation amount, all the modified pixels F, X in the large pixel group are first sorted according to the coordinate positions of the modified pixels F, X corresponding to the two-dimensional matrix, then the first 20 corrected pixels are selected by adopting a strategy of column scanning (row scan) or row scanning (column scan), for example, 20 correction pixels F having coordinates (1, 8), (1, 9), (1, 10), (2, 10), (2, 9), (2, 8), (2, 7), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10) …, (5, 5), (5, 6), etc. and error pixels X in fig. 19 are sequentially selected in a line scan manner as the first batch of correction pixels to be processed by the processor, and the second batch of correction pixels includes: and 20 corrected pixels F, X such as (5, 7), (5, 8), (6, 7), (6, 6), (6, 5), (6, 4), …, (9, 1), (9, 2). The next batch of 20 modified pixels F, X may be selected continuously in the manner described above until all modified pixels F, X in the large group of pixels have been selected.

In the two consecutively selected batches of modified pixels F, X, the first and second batches may each include at least two modified pixels in communication with each other, such that a later modified pixel may therefore affect an earlier modified pixel. Taking fig. 19 as an example, the correction pixels (6, 4) in the second batch and the correction pixels (5, 4) in the first batch are communicated with each other in the horizontal direction, but the two correction pixels (6, 4), (5, 4) are not simultaneously subjected to the processing, and the processing timing of the correction pixels (5, 4) in the first batch is earlier than the processing timing of the correction pixels (6, 4) in the second batch. In order to avoid the computation power of the processor being wasted by a later correction instead of an earlier correction, the 20 correction pixels F, X are divided into a dynamic allocation portion and a static allocation portion in step S74 of the third embodiment. The dynamic allocation is determined in part by the configuration of the first anchor point and the static allocation is determined in part by the configuration of the second anchor point. The dynamic configuration portion is similar to the anchor point configuration of step S64, and when the 0-1 integer program operation is performed in step S75, the first configuration values of the dynamic configuration portion can be adjusted, and the second configuration values of the static allocation portion are fixed values, which are not changed when the 0-1 integer program operation is performed in step S75. Setting strategies for these fixed values, for example: all of the second configuration values are set to 0, or set to 1, or set to a default 0-1 combination sequence, which is not limited by the invention. The invention is also not limited to the number of first configuration values and the number of second configuration values. Taking fig. 19 as an example, on the premise that the total number of the correction pixels is not more than 20, for example: the first arrangement value and the second arrangement value each correspond to 10 correction pixels, or the first arrangement value corresponds to 15 correction pixels and the second arrangement value corresponds to 5 correction pixels. In one embodiment, the correction pixels adjacent to the correction pixels of the previous batch are static allocation portions, the correction pixels not adjacent to the correction pixels of the previous batch are dynamic allocation portions, and taking fig. 19 as an example, the correction pixels (6, 4) in the second batch and the correction pixels (5, 4) in the first batch are communicated with each other in the horizontal direction, the correction pixels (7, 2) in the second batch are not communicated with the correction pixels (5, 4) in the first batch, so that the correction pixels (6, 4) belong to the static allocation portions, and the correction pixels (7, 2) belong to the dynamic allocation portions.

In step S75, the 0-1 integer program operation is executed according to each of the pixel groups, the maximum operand, the first anchor allocation and the second anchor allocation to generate a plurality of first modified results. Each of the first correction results indicates that one of the error pixel, the correction pixel, and the verification pixel is a high exposure or a low exposure. Step S75 is similar to step S65, in one embodiment, the correction results of step S65 correspond to all the error pixels, correction pixels and verification pixels in a pixel group, and the first correction results of step S75 correspond to a portion of the error pixels, correction pixels and verification pixels in a large pixel group.

In step S76, each of the first correction results is compared with one of the exposure states of the circuit diagram to generate a first comparison result indicating whether the first comparison result is qualified. Step S76 is similar to step S66.

In step S77, the histogram is updated according to the first comparison result and the first positioning point allocation of each of the pixel groups. Step S77 is similar to step S67, in one embodiment, step S67 updates the modified pixels F, X corresponding to the configuration values to the anchor map according to all the configuration values in the anchor configuration; in step S77, the modified pixels F, X corresponding to the first allocation values are updated to the histogram according to all the first allocation values in the first allocation point allocation.

Step S78 is "check whether a remaining number of the error pixels is greater than an allowable value". After the flow of steps S76 to S77 is performed once, some error pixels have disappeared because they were corrected. Therefore, after each correction, step S78 checks whether the number of error pixels remaining in a large pixel group is still larger than a tolerance. If the check result is "yes", it indicates that the remaining error pixels still need to be corrected, and therefore the process returns to step S74. If the check result is "no", it indicates that the number of remaining error pixels is less than or equal to the allowable value, and the correction may not be continued. In practice, there may be a failure of the correction pixel F, X in two consecutive correction results. In other words, the arrangement value of the modified pixel obtained at the k-th modification is different from the arrangement value of the modified pixel obtained at the k + 1-th modification. For example, for a correction pixel at a critical position of the adjacent region A, B, setting this correction pixel to 1 solves the correction of the a region but makes the correction of the B region unsatisfied; setting this pixel to 0 in turn solves the correction of the B region but makes the correction of the a region unsatisfied. The allowable value is set to ignore the excessive occupation of the computing resources of the processor by the repeatedly corrected correction pixels.

For clarity of explanation of the third embodiment, the flow after returning to step S74 will be described again. For convenience of description, the first anchor point configuration determined when step S74 is executed for the second time is referred to as a third anchor point configuration, the second anchor point configuration determined when step S74 is executed for the second time is referred to as a fourth anchor point configuration, the first correction result generated when step S75 is executed for the second time is referred to as a second correction result, and the first comparison result generated when step S76 is executed for the second time is referred to as a second comparison result.

In the second execution of step S74, the third anchor point configuration and the fourth anchor point configuration in the pixel group are determined according to the maximum computation amount. The third anchor configuration includes a plurality of third configuration values, the fourth anchor configuration includes a plurality of fourth configuration values, and the total number of the third configuration values and the total number of the fourth configuration values are associated with the maximum computation amount. It is noted that, in order to avoid the correction pixels and the error pixels from being repeatedly corrected, one of the correction pixels and the error pixels of the pixel group may be set to the second configuration value at the first timing, and set to the third configuration value at the second timing, the first timing being earlier than the second timing. In short, the same one or more correction pixels and error pixels are present in the plurality of correction pixels and error pixels selected twice in succession. For example, the first time step S74 is executed to select the 1 st to 100 th correction pixels and the error pixels, and the second time step S74 is executed to select the 51 st to 150 th pixels. The above numbers are merely illustrative and are not intended to limit the number of correction pixels that are repeatedly selected.

In the second execution of step S75, a 0-1 integer program operation is performed according to the pixel group, the maximum operand, the third anchor configuration, and the fourth anchor configuration to generate a plurality of second modified results. The 0-1 integer program operation performed in step S75 will dynamically change the third configuration values, and the fourth configuration values will not change during the 0-1 integer program operation. In the second execution of step S76, each second correction result is compared with an exposure status of the circuit diagram to generate a second comparison result. In the second execution of step S77, the localization map is updated according to the second comparison result and the third localization point configuration.

FIG. 20 is a system for generating and updating a histogram in accordance with an embodiment of the present invention. The system for generating and updating a localization profile comprises a non-transitory machine-readable storage device 1 and a processing device 3. The non-transitory machine-readable device 1 is configured to store a plurality of instructions. The processing device 3 is electrically connected to the non-transitory machine-readable storage device 1. The processing device 3 executes the instructions and causes operations comprising: generating at least one positioning distribution map according to a circuit diagram and at least one exposure pattern, wherein the circuit diagram comprises a plurality of target pixels and a plurality of background pixels, each positioning distribution map comprises a plurality of positioning points, and the positioning points are positioned in a plurality of the target pixels and are related to the exposure pattern; performing an exposure simulation according to each of the at least one positioning distribution map to generate at least one exposure result map, wherein the exposure simulation comprises simulating to emit a virtual light spot by each of the positioning points of each of the at least one positioning distribution map to generate at least one exposure result map; comparing the circuit diagram with the at least one exposure result diagram to generate at least one candidate error distribution diagram; selecting one of the at least one candidate error distribution map as an error distribution map, wherein the error distribution map comprises a plurality of error pixels; performing a 0-1 integer programming operation according to the circuit diagram and at least one of the error pixels to update one of the at least one localization profile, wherein the updated localization profile includes a plurality of modified localization points, and the updated localization profile is associated with the selected candidate error distribution map.

In one embodiment of the system for generating and updating a histogram, the target pixels form a circuit structure, each of the target pixels and the background pixels has an exposure status, the exposure status of each of the target pixels is a high exposure, and the exposure status of each of the background pixels is a low exposure.

In one embodiment of the system for generating and updating a localization profile, the at least one candidate error profile is a plurality of candidate error profiles, each of the candidate error profiles having a plurality of error pixel numbers; in the operations, selecting one of the at least one candidate error profiles as the error profile comprises: selecting a minimum value of the error pixel numbers; and using one of the at least one candidate error distribution map corresponding to the error pixel number with the minimum value as the error distribution map.

In one embodiment of the system for generating and updating a localization profile, in the operations, performing the 0-1 integer program operation according to the circuit diagram and at least one of the error pixels to update one of the at least one localization profile comprises: selecting the at least one error pixel of the error distribution map to perform a dilation operation to determine a plurality of correction pixels in the localization map; performing the dilation operation on each of the modified pixels to determine a plurality of verification pixels in the histogram; and performing the 0-1 integer programming operation according to the circuit diagram, the at least one error pixel, the correction pixels and the verification pixels to update the at least one of the at least one histogram.

In one embodiment of the system for generating and updating a histogram, in the operations, performing the 0-1 integer program operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the one of the at least one histogram includes: generating a fixed-point configuration according to the at least one error pixel and the correction pixels; executing the 0-1 integer programming operation according to the at least one error pixel, the correction pixels and the positioning point configuration to generate a plurality of correction results; comparing each of the correction results with one of the exposure states of the circuit diagram to generate a comparison result, wherein each of the correction results indicates that each of the at least one error pixel, the correction pixels, and the verification pixels is a high exposure or a low exposure; and updating the at least one positioning distribution map according to the comparison result and the positioning point configuration.

In one embodiment of the system for generating and updating a histogram, the selecting the at least one error pixel of the error histogram to perform the dilation operation to determine the modified pixels in the histogram includes: performing the dilation operation on each error pixel of the error distribution map to determine the correction pixels in the localization distribution map; performing the dilation operation to determine the verification pixels in the histogram based on each of the correction pixels includes: executing a connected component marking program according to each correction pixel to determine a plurality of pixel groups; and performing the dilation operation on each of the plurality of pixel clusters to determine the verification pixels in the histogram; generating a fixed-point configuration according to each error pixel and each correction pixel in each pixel group; performing the 0-1 integer programming operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the at least one histogram, including: executing the 0-1 integer programming operation according to each pixel group and each anchor point configuration to generate a plurality of correction results; comparing each of the correction results of each of the pixel groups with one of the exposure states of the circuit diagram to generate a comparison result, wherein each of the correction results indicates that at least one of the error pixels, each of the correction pixels and each of the verification pixels is a high exposure or a low exposure; and updating the at least one positioning distribution map according to the comparison results and the positioning point configuration of each pixel group.

In one embodiment of the system for generating and updating a histogram, the selecting the at least one error pixel of the error histogram to perform the dilation operation to determine the modified pixels in the histogram includes: performing the dilation operation on each of the error pixels of the error map to determine the correction pixels in the localization map; performing the dilation operation on each of the modified pixels to determine the verification pixels in the histogram includes: executing a connected component marking program according to each correction pixel to determine a plurality of pixel groups; and performing the dilation operation on each of the plurality of pixel clusters to determine the verification pixels in the histogram; determining a first positioning point configuration and a second positioning point configuration in each pixel group according to a maximum operation amount; performing the 0-1 integer programming operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the at least one histogram, including: executing the 0-1 integer programming operation according to each of the pixel groups, the maximum operand, the first anchor point configuration and the second anchor point configuration to generate a plurality of first correction results; comparing each of the first correction results of each of the pixel groups with one of the exposure states of the circuit diagram to generate a first comparison result, wherein each of the first correction results indicates that at least one of the error pixels, each of the correction pixels and each of the verification pixels is a high exposure or a low exposure; and updating the at least one positioning distribution map according to the first comparison results and the first positioning point configurations of each pixel group.

In an embodiment of the system for generating and updating the histogram, in the operations, after updating the one of the at least one histogram according to the first comparison results and the first anchor point assignments of each of the pixel groups, the method further includes: checking a remaining number of the error pixels in one of the pixel groups; when the residual quantity is larger than an allowable value, determining a third positioning point configuration and a fourth positioning point configuration in the pixel group to be checked according to the maximum operand; executing the 0-1 integer programming operation according to the checked pixel group, the maximum operand, the third anchor point configuration and the fourth anchor point configuration to generate a plurality of second correction results; comparing each second correction result with one of the exposure states of the circuit diagram to generate a second comparison result; updating the positioning distribution map according to the second comparison result and the third positioning point configuration; wherein the third anchor point configuration comprises a plurality of third configuration values, the 0-1 integer program operation dynamically changing the third configuration values; the fourth anchor configuration comprises a plurality of fourth configuration values that are invariant in the 0-1 integer program operation; and the total number of the third configuration values and the fourth configuration values is related to the maximum operand.

In one embodiment of the system for generating and updating a histogram, in the operations, one of the modified pixels of the pixel group is set to the second configuration value at a first timing and is set to the third configuration value at a second timing, and the first timing is earlier than the second timing.

In one embodiment of the system for generating and updating a localization profile, each of the target pixels and the background pixels has a length or width less than a diameter of the virtual spot.

In an embodiment of the system for generating and updating the localization profiles, a distance between two of the localization points is not less than a length or a width of one of the target pixels.

In an embodiment of the system for generating and updating the histogram, each of the at least one exposure result map includes a plurality of trial exposure results, each of the trial exposure results corresponds to one of the target pixels and the background pixels, and each of the error pixels corresponds to one of the trial exposure results; wherein when one of the error pixels corresponds to one of the target pixels, one of the trial exposure results corresponding to the one of the error pixels is a low exposure; and when one of the error pixels corresponds to one of the background pixels, the other of the trial exposure results corresponding to the one of the error pixels is high exposure.

In summary, the method and system for generating and updating the histogram of the present invention pre-find the initial position map of the light spot through exposure simulation, and apply connected component labeling and parallelization integer programming operation, so as to effectively reduce the operation amount and speed up the calculation. The invention can realize the exposure by using the light spots with the size larger than the line width so as to meet the precision requirements of fine line width and line distance.

The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method of generating and updating a histogram, comprising:

generating at least one positioning distribution map according to a circuit diagram and at least one exposure pattern, wherein the circuit diagram comprises a plurality of target pixels and a plurality of background pixels, each positioning distribution map comprises a plurality of positioning points, and the positioning points are positioned in a plurality of the target pixels and are associated with the exposure pattern;

performing exposure simulation according to each of the at least one positioning distribution map to generate at least one exposure result map, wherein the exposure simulation comprises simulating to emit virtual light spots by each of the positioning points of each of the at least one positioning distribution map to generate at least one exposure result map;

comparing the circuit diagram with the at least one exposure result diagram to generate at least one candidate error distribution diagram;

selecting one of the at least one candidate error distribution map as an error distribution map, wherein the error distribution map comprises a plurality of error pixels; and

performing a 0-1 integer programming operation according to the circuit diagram and at least one of the error pixels to update one of the at least one localization profile, wherein the updated localization profile includes a plurality of modified localization points, and the updated localization profile is associated with the selected candidate error distribution map.

2. The method as claimed in claim 1, wherein the target pixels form a circuit structure, each of the target pixels and the background pixels has an exposure status, the exposure status of each of the target pixels is a high exposure, and the exposure status of each of the background pixels is a low exposure.

3. The method of claim 1, wherein the at least one candidate error distribution map is a plurality of candidate error distribution maps, each of the candidate error distribution maps having a plurality of error pixel counts; selecting one of the at least one candidate error distribution map as the error distribution map comprises:

selecting the minimum value of the error pixel numbers; and

and taking one of the at least one candidate error distribution map corresponding to the error pixel number with the minimum value as the error distribution map.

4. The method of claim 2, wherein performing the 0-1 integer program operation to update one of the at least one histogram according to the circuit diagram and at least one of the error pixels comprises:

selecting the at least one error pixel of the error map to perform a dilation operation to determine a plurality of correction pixels in the at least one location map;

performing the dilation operation on each of the modified pixels to determine a plurality of verification pixels in the at least one histogram; and

performing the 0-1 integer programming operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the one of the at least one histogram.

5. The method of claim 4, wherein performing the 0-1 integer program operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the one of the at least one histogram includes:

generating an anchor point configuration according to the at least one error pixel and the correction pixels;

executing the 0-1 integer programming operation according to the at least one error pixel, the correction pixels and the positioning point configuration to generate a plurality of correction results;

comparing each of the correction results with one of the exposure states of the circuit diagram to generate a comparison result, wherein each of the correction results indicates that each of the at least one error pixel, the correction pixels and the verification pixels is a high exposure or a low exposure; and

updating the one of the at least one positioning distribution map according to the comparison result and the positioning point configuration.

6. The method of claim 4, wherein selecting the at least one error pixel of the error map to perform the dilation operation to determine the modified pixels in the histogram comprises: performing the dilation operation on each of the error pixels of the error map to determine the correction pixels in the localization map;

performing the dilation operation to determine the verification pixels in the at least one histogram based on each of the correction pixels includes: executing a connected component marking program according to each correction pixel to determine a plurality of pixel groups; and performing the dilation operation on each of the plurality of pixel clusters to determine the verification pixels in the at least one of the positioning profiles;

generating an anchor point configuration according to each error pixel and each correction pixel in each pixel group;

performing the 0-1 integer programming operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the at least one histogram, including: executing the 0-1 integer programming operation according to each pixel group and each anchor point configuration to generate a plurality of correction results; comparing each of the correction results of each of the pixel groups with one of the exposure states of the circuit diagram to generate a comparison result, wherein each of the correction results indicates that each of the at least one error pixel, the correction pixels and the verification pixels is a high exposure or a low exposure; and updating the at least one positioning distribution map according to the comparison results of the pixel groups and the positioning point configuration.

7. The method of claim 4, wherein selecting the at least one error pixel of the error map to perform the dilation operation to determine the modified pixels in the histogram comprises: performing the dilation operation on each of the error pixels of the error map to determine the correction pixels in the localization map;

determining a first anchor point configuration and a second anchor point configuration in each of the pixel groups according to the maximum computation amount, wherein the first anchor point configuration comprises a plurality of first configuration values, and the 0-1 integer programming operation dynamically changes the first configuration values; the second anchor point configuration comprises a plurality of second configuration values, and the second configuration values are not changed in the 0-1 integer programming operation; and the total number of the first configuration values and the second configuration values is related to the maximum operation amount;

performing the 0-1 integer programming operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the at least one histogram, including: executing the 0-1 integer programming operation according to each of the pixel groups, the maximum operand, and the first anchor point configuration and the second anchor point configuration in each of the pixel groups to generate a plurality of first correction results; comparing each of the first correction results of each of the pixel groups with one of the exposure states of the circuit diagram to generate a first comparison result, wherein each of the first correction results indicates whether each of the at least one error pixel, the correction pixels, and the verification pixels is a high exposure or a low exposure; and updating the one of the at least one positioning distribution map according to the first comparison result and the first positioning point configuration of each of the pixel groups.

8. The method of claim 7, further comprising, after updating the one of the at least one histogram according to the first comparison results and the first anchor point assignments of each of the pixel groups:

checking the remaining number of the error pixels in one of the pixel groups;

when the residual quantity is larger than the allowable value, determining a third positioning point configuration and a fourth positioning point configuration in the pixel group to be checked according to the maximum operand;

executing the 0-1 integer programming operation according to the inspected pixel group, the maximum operand, the third anchor point configuration and the fourth anchor point configuration to generate a plurality of second correction results;

comparing each second correction result with one of the exposure states of the circuit diagram to generate a second comparison result; and

updating the at least one positioning distribution map according to the second comparison result and the third positioning point configuration; wherein the content of the first and second substances,

the third anchor configuration comprises a plurality of third configuration values, and the 0-1 integer program operation dynamically changes the third configuration values;

the fourth anchor configuration comprises a plurality of fourth configuration values that are invariant in the 0-1 integer program operation; and

the total number of the third configuration values and the fourth configuration values is associated with the maximum computation amount.

9. The method of claim 8, wherein one of the modified pixels of the inspected pixel group is set to the second configuration value at a first timing, is set to the third configuration value at a second timing, and is earlier than the second timing.

10. The method of claim 1, wherein each of the target pixels and the background pixels has a length or width less than a diameter of the virtual spot.

11. The method of claim 1, wherein a distance between two of the anchor points is not less than a length or a width of one of the target pixels.

12. The method of claim 1, wherein each of the at least one exposure result map comprises a plurality of trial exposure results, each of the trial exposure results corresponds to one of the target pixels and the background pixels, and each of the error pixels corresponds to one of the trial exposure results; wherein

When one of the error pixels corresponds to one of the target pixels, one of the trial exposure results corresponding to the one of the error pixels is a low exposure; and

when one of the error pixels corresponds to one of the background pixels, the other of the trial exposure results corresponding to the one of the error pixels is a high exposure.

13. A system for generating and updating a histogram includes a non-transitory machine-readable storage device storing a plurality of instructions; and a processing device electrically coupled to the non-transitory machine-readable storage device, the processing device executing the instructions and causing operations comprising:

generating at least one positioning distribution graph according to a circuit diagram and at least one exposure pattern, wherein the circuit diagram comprises a plurality of target pixels and a plurality of background pixels, each positioning distribution graph comprises a plurality of positioning points, and the positioning points are located in a plurality of the target pixels and are related to the exposure pattern;

14. The system for generating and updating a histogram of claim 13, wherein the target pixels form a circuit structure, each of the target pixels and the background pixels has an exposure status, the exposure status of each of the target pixels is a high exposure, and the exposure status of each of the background pixels is a low exposure.

15. The system for generating and updating a localization profile of claim 13, wherein the at least one candidate error profile is a plurality of candidate error profiles, each of the plurality of candidate error profiles having a plurality of error pixel counts; in the operations, selecting one of the at least one candidate error profiles as the error profile comprises:

selecting the minimum value of the error pixel numbers; and

16. The system for generating and updating a histogram of claim 14, wherein the performing the 0-1 integer program operation to update one of the at least one histogram according to the circuit diagram and at least one of the error pixels comprises:

17. The system for generating and updating a histogram of claim 16, wherein the operations of performing the 0-1 integer program operation based on the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the one of the at least one histogram of operations includes:

18. The system for generating and updating a histogram of claim 16, wherein the operations of selecting the at least one error pixel of the error histogram to perform the dilation operation to determine the modified pixels in the histogram comprise: performing the dilation operation on each of the error pixels of the error map to determine the correction pixels in the localization map;

performing the dilation operation to determine the verification pixels in the at least one histogram based on each of the correction pixels includes:

executing a connected component marking program according to each correction pixel to determine a plurality of pixel groups; and

performing the dilation operation on each of the plurality of pixel clusters to determine the verification pixels in the at least one of the positioning profiles;

performing the 0-1 integer programming operation according to the circuit diagram, the at least one error pixel, the correction pixels, and the verification pixels to update the at least one histogram, including:

executing the 0-1 integer programming operation according to each pixel group and each anchor point configuration to generate a plurality of correction results;

comparing each of the correction results of each of the pixel groups with one of the exposure states of the circuit diagram to generate a comparison result, wherein each of the correction results indicates that each of the at least one error pixel, the correction pixels and the verification pixels is a high exposure or a low exposure; and

updating the one of the at least one anchor distribution map according to the comparison results of the pixel groups and the anchor point configuration.

19. The system for generating and updating a histogram as claimed in claim 16, wherein the selecting the at least one error pixel of the error histogram to perform the dilation operation to determine the modified pixels in the histogram comprises: performing the dilation operation on each of the error pixels of the error map to determine the correction pixels in the localization map;

determining a first positioning point configuration and a second positioning point configuration in each of the pixel groups according to the maximum operand, wherein the first positioning point configuration comprises a plurality of first configuration values, and the 0-1 integer programming operation dynamically changes the first configuration values; the second anchor point configuration comprises a plurality of second configuration values, and the second configuration values are not changed in the 0-1 integer programming operation; and the total number of the first configuration values and the second configuration values is related to the maximum operation amount;

executing the 0-1 integer programming operation according to each of the pixel groups, the maximum operand, and the first anchor point configuration and the second anchor point configuration in each of the pixel groups to generate a plurality of first correction results;

comparing each of the first correction results of each of the pixel groups with one of the exposure states of the circuit diagram to generate a first comparison result, wherein each of the first correction results indicates that at least one of the error pixels, each of the correction pixels and each of the verification pixels is a high exposure or a low exposure; and

updating the at least one positioning distribution map according to the first comparison results and the first positioning point configurations of each pixel group.

20. The system for generating and updating a histogram of claim 19, wherein, during the operations,

after updating the at least one histogram according to the first comparison results and the first anchor configurations of each of the pixel groups, the method further includes:

checking the remaining number of the error pixels in one of the pixel groups;

executing the 0-1 integer programming operation according to the checked pixel group, the maximum operand, the third anchor point configuration and the fourth anchor point configuration to generate a plurality of second correction results;

updating the at least one positioning distribution map according to the second comparison result and the third positioning point configuration; wherein

21. The system for generating and updating a histogram of claim 20, wherein in the operations, one of the modified pixels of the pixel group being examined is set to the second configuration value at a first timing and is set to the third configuration value at a second timing, and the first timing is earlier than the second timing.

22. The system for generating and updating a histogram of claim 13, wherein each of the target pixels and the background pixels has a length or width smaller than a diameter of the virtual spot.

23. The system for generating and updating the histogram of claim 13, wherein a distance between two of the anchor points is not less than a length or a width of one of the target pixels.

24. The system for generating and updating a histogram of claim 13, wherein each of the at least one exposure result map includes a plurality of trial exposure results, each of the trial exposure results corresponding to one of the target pixels and the background pixels, and each of the error pixels corresponding to one of the trial exposure results; wherein